Microsoft faces stiff penalties in Europe for failing to give customers there an adequate choice of Web browsers in its Windows operating systems, and now it is being chased by the Danish tax authority as well.

The European Commission ruled last year that Microsoft failed to comply with an order to give customers a clear choice of using something other than Internet Explorer for their browser during setup of Windows machines.

Due to what Microsoft says is a technical error, millions of Windows PCs shipped in Europe that didn’t serve up a browser-choice screen, which the EC says flouted its order.

The fine for this failure could be upward of $7 billion, but when it is actually issued sometime this week it is expected to be less.

Meanwhile, Denmark says that Microsoft played fast-and-loose with the value of a Danish company it bought then sold to another Microsoft entity in Ireland. As a result, Denmark claims missed out on $1 billion in taxes it could have collected if the company had been sold for its true value, according to a Danish news report.

The company involved is Navison, which makes enterprise resource planning software that is one of the four main products of Microsoft’s Dynamics software package, and which is now sold under the name Dynamics NAV. The former Navison is based north of Copenhagen and employs 600 people, the report says.

According to the Danish news site DR, the Danish treasury seeks $1 billion from Microsoft, the largest single tax claim the treasury has ever made.

Microsoft bought Navison in 2002 for $1.45 billion. Shortly thereafter Microsoft sold it to its Irish subsidiary, according to DR. But the Danish treasury claims the price was less than the actual value of Navison, meaning Microsoft paid less in taxes on the sale than it would have if it had been sold for full value, just as if it had been sold to a third party rather than a subsidiary.

“The internal trade must therefore be at the same price as two independent companies would agree on,” the DR story says. “Otherwise, the groups use this method to move profits in tax havens.”